Here is the full list of all 18 Galcon Legends achievements.
Campaign completed at Commander or higher rank.
Campaign completed at Lieutenant or higher rank.
Campaign completed at Ensign or higher rank.
Campaign completed at Cabin Boy or higher rank.
Defeated the Slug Princess.
Defeated Zanthor.
Defeated the Banjo King.
Defeated the Phantom.
Defeated the Crab Lord.
Defeated Ms. Magpie.
Defeated Walter.
Tutorial completed.
Campaign completed at Captain or higher rank.
Campaign completed at Admiral or higher rank.
Campaign completed at 1-Stripe Admiral or higher rank.
Campaign completed at 2-Stripe Admiral or higher rank.
Campaign completed at 3-Stripe Admiral or higher rank.
Campaign completed at Grand Admiral rank.